### Table 10: Comparing N-elites GA with other approaches for the biomodeling problem

"... In PAGE 30: ... The E ect of Elitism To study the e ect of elitism in our simplex-GA hybrid, we applied a real-coded GA with N elites (where N is the number of variables to be optimized) to the biomodeling problem and to the function maximization problem. Table10 shows the average nal best tness for the biomodeling problem. For ease of comparison, we also included results of three other alternative approaches: the real-coded GA, our hybrid, and the R-B hybrid.... In PAGE 30: ... Therefore, it is in fact a GA with 1 elite. Table10 shows that the real-coded GA with N elites improved, on the average, the nal best tness of the real-coded GA with 1 elite by 50% for the biomodeling problem. This is about half of the overall performance improvement of our 45% hybrid.... ..."

### Table 2. A schedule for the benchmark problem in Table 1 with the makespan = 293 In the next section, we introduce the three evolutionary based heuristics we implemented and ran with OSSP benchmark problems taken from a well known source of test problems. 3 Genetic Algorithms for OSSP In this work, we use three genetic algorithms. We start our discussion by pre- senting the Permutation GA and then turn our attention to the Hybrid GA.

"... In PAGE 3: ... Most benchmark problems in the literature of scheduling have this property. A schedule to the problem instance of Table 1 is given in Table2 . We note that the operations are not scheduled in their order of appearance in Table 1.... In PAGE 3: ... We note that the operations are not scheduled in their order of appearance in Table 1. Thus, operation O32, for instance, is scheduled at time 78 while operation O31 is scheduled at time 226, as can be seen in Table2 . Operation O22 is the last one to nish, with \end time quot; equal to 293, thus, the makespan of the schedule given in Table 2 is 293, which happens to be the optimal solution for this problem.... In PAGE 3: ... Thus, operation O32, for instance, is scheduled at time 78 while operation O31 is scheduled at time 226, as can be seen in Table 2. Operation O22 is the last one to nish, with \end time quot; equal to 293, thus, the makespan of the schedule given in Table2 is 293, which happens to be the optimal solution for this problem. Machines Job J1 Job J2 Job J3 Job J4 M1 85 23 39 55 M2 85 74 56 78 M3 3 96 92 11 M4 67 45 70 75 Table 1.... ..."

### Table 1 Final designs comparison of GA and the hybrid OC-GA

2005

"... In PAGE 6: ...he optimal design process was carried out using a Pentium 4 3.0GHz computer with 512 MB memory. Since the GA and the hybrid OC-GA are stochastic algorithms, three separate runs were conducted respectively for each method with randomly generated initial designs. A comparison of the total tonnage of steel material required for the final best-fit designs of these runs is summarized in Table1 . The second column of the Table gives the structural weight of the framework.... In PAGE 6: ... When a drift response ratio is less than or equal to 1, the corresponding drift constraint is deemed feasible; otherwise a violation in the constraint is found. As shown in Table1 , the hybrid OC-GA method was able to obtain much better quality solutions than the GA method in terms of both the minimum value of the structure weight and drift response performance. On average, the OC-GA achieved a minimum structural weight of 5887 kN, while the GA was unable to obtain a feasible design even at a significantly higher average minimum weight of 7093 kN.... ..."

### Table 2: Di erent types of algorithms considered Name Selection Penalty GA linear ranking p + elitism EGA linear ranking

"... In PAGE 5: ... If the two penalty param- eters are the same and linear ranking is removed, the algorithm is denoted ES(m + m). Table2 summarizes the algorithms compared in this study. Table 2: Di erent types of algorithms considered Name Selection Penalty GA linear ranking p + elitism EGA linear ranking... ..."

### Table 6. Comparisons of the approaches (Hybrid GA: genetic algorithm + local search; Hybrid VNS: iterated variable neighborhood search, and our approaches) on the problem. Hybrid GA Hybrid VNS Decomposition

2005

"... In PAGE 5: ...enalties are re-assigned and the descent local search is started again. See [10] for more details. Using the decomposition, construction and post-processing approach, we obtained a number of different schedules on the problem presented in Section 2. The best results out of 5 runs on each of the approaches, namely the hybrid genetic algorithm, the variable neighborhood search and our approach with and without the variable neighborhood search approach as the 3rd stage of post-processing, are presented in Table6 . The values in parentheses give the computational time of the corresponding approaches.... ..."

Cited by 3

### Table 6. Comparisons of the approaches (Hybrid GA: genetic algorithm + local search; Hybrid VNS: iterated variable neighborhood search, and our approaches) on the problem. Hybrid GA Hybrid VNS Decomposition

2005

"... In PAGE 5: ...enalties are re-assigned and the descent local search is started again. See [10] for more details. Using the decomposition, construction and post-processing approach, we obtained a number of different schedules on the problem presented in Section 2. The best results out of 5 runs on each of the approaches, namely the hybrid genetic algorithm, the variable neighborhood search and our approach with and without the variable neighborhood search approach as the 3rd stage of post-processing, are presented in Table6 . The values in parentheses give the computational time of the corresponding approaches.... ..."

Cited by 3

### Table 2. Algorithm Framework for GA-DFALS Algorithm: Learning Deterministic Finite-state Automaton Based on Genetic Algorithm (A Basis)

2006

"... In PAGE 8: ...dure [7], and it is so called standard genetic algorithm 4. The core of our learning system (Deterministic Finite-state Automaton Learning System Based on Genetic Algorithm, GA-DFALS) is based on this framework (see Table2 ). The genetic operators we used are fitness proportionate selection operator, uniform crossover operator, and point mutation operator.... ..."

### Table 9: Performance of GA-TS hybrid with clustering

"... In PAGE 10: ... The second advantage of using clustering, as mentioned before, is that the solution space is reduced, thus the GA is capable of exploring the solution space more e ectively. Table9 and Figure 5 present a comparison between GA- TS hybrid and CGA-TS which uses clustering for initial population of solutions. Results obtained indicate that the clustered based technique produces solutions that are at least 20% better than those obtained based on the original circuit representation for medium and large circuits.... ..."

### Table 5: Results for BK instances: average percent errors with respect to the optima and average running times of HYBRID (with 32 iterations and 10 elite solutions).

"... In PAGE 8: ... Each subclass contains 10 instances built with the exact same parameters (such as number of elements and cost distribution), just with different random seeds. Table5 presents the results for BK: for each subclass, we present the average error obtained by the algorithm and the average running time.... ..."